Determine whether the relation represents a function. If it is a function, state the domain and range.

Select all points that are on the graph of the line

Marysya12 [62]

Answer:

0,3

Step-by-step explanation:

Well 0,3 is the only one that is on here... I apologize if I am wrong!

7 0

3 years ago

5.

GarryVolchara [31]

$The\ volume\ of\ cylinder:V=\pi r^2 h\\\\r-radius;\ h-height\\---------------------------\\\\r=4cm;\ h=4cm\\\\therefore\\\\\boxed{V=\pi\cdot4^2\cdot4=64\pi\ (cm^3)}\leftarrow answer$

5 0

3 years ago

Read 2 more answers

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

3 years ago

Use elimination to solve each system of equations 2x-y=-1 3x-2y=1

mixer [17]

$2x-y=-1 \ \ \ |\times (-2) \\
3x-2y=1 \\ \\
-4x+2y=2 \\
\underline{3x-2y=1 \ \ \ \ } \\
-4x+3x=2+1 \\
-x=3 \ \ \ |\times (-1) \\
x=-3 \\ \\
2x-y=-1 \\
2 \times (-3)-y=-1 \\
-6-y=-1 \ \ \ |+6 \\
-y=5 \ \ \ |\times (-1) \\
y=-5 \\ \\
\boxed{(x,y)=(-3,-5)}$